Under PCFM, if the manufacturer carries out production according to [Q.sup.*.sub.2], the optimal loan amount is as follows:
Considering the goal of maximizing profit of the whole supply chain and the profits under the conditions of no capital constraint, RPFM and PCFM are compared.
Under PCFM, similarly, [Q.sup.*.sub.2] > [Q.sub.N].
In addition, the manufacturer's maximum production volume is [Q.sup.*.sub.2] = [F.sup.-1](1 - c/[omega]) under PCFM. According to the assumption, [Q.sup.*.sub.2] = [F.sup.-1](1 - c/[omega]) > [Q.sub.N], and the loan amount is [K.sup.*.sub.2] = c[F.sup.-1](1 - c/[omega]) - [beta].
If the secondary financing is needed when their own capital could not satisfy the second-order demand, the manufactures need the second financing, and the loan interest rate meets certain requirements, the RPFM can increase production volume of the manufacturer and increase profit of the entire supply chain; the corresponding conclusion can also be reached under PCFM. By comparing these two financing modes, the whole supply chain performance is better than that with financing from a commercial bank by PCFM.
Under the PCFM, from (33) and (34), [Q.sup.*.sub.2] = [F.sup.-1] (1 - c/[omega]) is verified satisfying the conditions; in this case, we have [Q.sup.*.sub.2] = 533.
Figure 6 shows that, under the RPFM, profits of the supply chain are more than those under classic "newsvendor" model and the PCFM. For 1/3 < [alpha] < 7/9, profits of the supply chain can reach the maximum value and will decrease with increase of discount coefficient [alpha], which also indicates that the larger discount will lead to higher profit of the supply chain.
The manufacturer with capital constraint could finance through the retailer's prepayment financing mode (RPFM) and the procurement contract financing mode (PCFM).
Through our analysis, the result shows that when the discount coefficient meets certain requirements, profits of the manufacturer, retailer, and the entire supply chain can all increase and will be generally superior to those under the PCFM. The optimal production volume of the manufacturer is greater than that with its own capital under the PCFM.
Moreover, the profit level under RPFM is higher than PCFM; it reveals why manufacturer prefers to select inner financing mode such as RPFM compared to external finance mode from a commercial bank.